In oil and gas exploration, electrical properties of the earth formations are commonly measured to provide useful clues about the materials composing the formations, such as the presence or absence of oil-bearing structures near a borehole. Techniques for measuring electrical properties of earth formations include lowering an instrument into the borehole to obtain the measurements. The instrument may be positioned in the borehole after the drill bit is removed, which is often referred to as “wireline logging.” Alternatively, an instrument is included in the drill string to acquire measurements while the borehole is being drilled, which is often referred to as “measurement-while-drilling” (MWD) or “logging-while-drilling” (LWD).
Instruments utilized by MWD/LWD techniques include “wave resistivity tools” that transmit an electromagnetic wave with at least one interrogation frequency into the surrounding formation. The attenuation and/or phase shift of the wave is measured by two spaced receivers to estimate an electrical property such as the resistivity and/or dielectric constant of the formation. The interrogation frequencies of wave resistivity tools are commonly selected from the range 400 kHz to 2 MHz, although other interrogation frequencies may be utilized.
Wireline logging techniques commonly employ “inductive resistivity tools” or, alternatively, “galvanic resistivity tools.” Inductive resistivity tools generate an AC magnetic field with a selected interrogation frequency in the surrounding formation to induce an alternating current through the formation. A receiver system measures the perturbations to the AC field caused by the alternating current to derive an estimate of the resistivity of the surrounding formation. Galvanic resistivity tools inject current having a selected interrogation frequency directly into a formation to measure the resistivity. Interrogation frequencies employed by inductive and galvanic resistivity tools are commonly selected from the range 100 Hz to 100 kHz. Typical interrogation frequencies employed by inductive and galvanic tools are usually not sufficiently high to determine dielectric properties of the earth formation.
Resistivity measurements obtained by MWD/LWD techniques sometimes do not agree with measurements obtained by wireline logging techniques. Discrepancies are sometimes attributable to the deteriorating conditions of the borehole and surrounding environment affecting wireline logging techniques, which are typically performed long after the borehole has been drilled. However, frequency dispersion can be another factor that can adversely affect the correlation of resistivity measurements obtained by MWD/LWD and wireline logging, given that the two types of techniques typically employ different interrogation frequencies. In this context, frequency dispersion refers a situation where certain materials in a medium respond differently to different interrogation frequencies. In certain earth formations, frequency dispersion has been observed to cause a higher resistivity to be measured with lower interrogation frequencies.
There is therefore a need for a technique that adjusts for the effects of frequency dispersion on electromagnetic wave well logging data. Advantageously, this technique would compensate for the effects of frequency dispersion, allowing more effective correlation of data obtained by tools employing different interrogation frequencies. Preferably, the technique could also be applied directly to existing logging data without requiring extensive knowledge of formation properties.